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3 years ago

Find the measure of the largest angle in the triangle

Mathematics

1 answer:

tester [92]3 years ago

5 0

Answer:

72°

Step-by-step explanation:

Find the image of the question attached

The sum of angle in a triangle is 180°

Hence:

15x+24x+21x = 180°

60x =180

x =180/60

x= 3

Get the largest angle

The largest angle out of the angles is 24x

24x =24(3)

24(3) =72°

Hence the measure of the largest angle is 72°

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Determine which function has the greatest rate of change over the interval [0, 2].

ruslelena [56]

Remember that the average rate of change of a function over an interval is the slope of the straight line connecting the end points of the interval. To find those slopes, we are going to use the slope formula: $m= \frac{y_{2}-y_{1}}{x_2-x_1}$

Rate of change of $a$ :
From the graph we can infer that the end points are (0,1) and (2,4). So lets use our slope formula to find the rate of change of $a$ :
$m= \frac{y_{2}-y_{1}}{x_2-x_1}$
$m= \frac{4-1}{2-0}$
$m= \frac{3}{2}$
$m=1.5$
The average rate of change of the function $a$ over the interval [0,2] is 1.5

Rate of change of $b$ :
Here the end points are (0,0) and (2,2)
$m= \frac{2-0}{2-0}$
$m= \frac{2}{2}$
$m=1$
The average rate of change of the function $b$ over the interval [0,2] is 1

Rate of change of $c$ :
Here the end points are (0,-1) and (2,0)
$m= \frac{0-(-1)}{2-0}$
$m= \frac{1}{2}$
$m=0.5$
The average rate of change of the function $c$ over the interval [0,2] is 0.5

Rate of change of $d$ :
Here the end points are (0,0.5) and (2,2.5)
$m= \frac{2.5-0.5}{2-0}$
$m= \frac{2}{2}$
$m=1$
The average rate of change of the function $d$ over the interval [0,2] is 1

We can conclude that the <span>function that has the greatest rate of change over the interval [0, 2] is the function a.</span>

4 0

3 years ago

Which equations represent the line that is parallel to 3x − 4y = 7 and passes through the point (−4, −2)? Select two options.

Elanso [62]

Answer:

2 and 5

Step-by-step explanation:

The slope-intercept form of a line is y=mx-b where m is slope and b is y-intercept.

The point-slope form of a line is y-y1=m(x-x1) where m is the slope and (x1,y1) is a point on the line.

The standard form a line is ax+by=c.

So anyways parallel lines have the same slope.

So if we are looking for a line parallel to 3x-4y=7 then we need to know the slope of this line so we can find the slope of our parallel line.

3x-4y=7

Goal: Put into slope-intercept form

3x-4y=7

Subtract 3x on both sides:

-4y=-3x+7

Divide both sides by -4:

$y=\frac{-3}{-4}x+\frac{7}{-4}$

Simplify:

$y=\frac{3}{4}x+\frac{-7}{4}$

So the slope of this line is 3/4. So our line that is parallel to this one will have this same slope.

So we know our line should be in the form of $y=\frac{3}{4}x+b$ .

To find b we will use the point that is suppose to be on our new line here which is (x,y)=(-4,-2).

So plugging this in to solve for b now:

$-2=\frac{3}{4}(-4)+b$

$-2=-3+b$

$3-2=b$

$b=1$

so the equation of our line in slope-intercept form is $y=\frac{3}{4}x+1$

So that isn't option 1 because the slope is different. That was the only option that was in slope-intercept form.

The standard form of a line is ax+by=c and we have 2 options that look like that.

So let's rearrange the line that we just found into that form.

$y=\frac{3}{4}x+1$

Clear the fractions because we only want integer coefficients by multiplying both sides by 4.

This gives us:

$4y=3x+4$

Subtract 3x on both sides:

$-3x+4y=4$

I don't see this option either.

Multiply both sides by -1:

$3x-4y=-4$

I do see this as a option. So far the only option that works is 2.

Let's look at point slope form now.

We had the point that our line went through was (x1,y1)=(-4,-2) and the slope,m, was 3/4 (we found this earlier).

y-y1=m(x-x1)

Plug in like so:

y-(-2)=3/4(x-(-4))

y+2=3/4 (x+4)

So option 5 looks good too.

7 0

3 years ago

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Please help with this question.

Alchen [17]

Answer:

-9

Step-by-step explanation:

6 0

2 years ago

What number must you multiply both sides of 3/4a=24 by to get equivalent equation a=32??

Mamont248 [21]

4 because 4 times 24 equals 96 then 96 divided by 3 equals 32

3 0

3 years ago

2r/5+7r/15= rewrite the expression by collecting like terms

kramer

<span>2r/5+7r/15=
LCM=15
(15\5=3*2r=6r)
15\15=1*7r=7r
answer=6r+7r\15
answer=13r\15</span>

3 0

3 years ago

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